Variation of parameters - i have different particular soluti

  • Thread starter omar yahia
  • Start date
  • #1
omar yahia
9
0
i was trying to get a particular solution of a 3rd order ODE using the variation of parameters method
the homogeneous solution is yh = c1 e-x + c2 ex + c3 e2x
the particular solution is yp=y1u1+y2u2+y3u3
as u1=∫ (w1 g(x) /w) dx , u2=∫ (w2 g(x) /w) dx , u3=∫ (w3 g(x) /w) dx
w =
|y1 y2 y3|
|y'1 y'2 y'3|
|y''1 y''2 y''3|

when i choose y1 , y2 , y3 to be e-x,ex,e2x i get an answer ,
but when i change the arrangement (like: ex,e-x,e2x )
i get another different answer !

so , i have two questions
1 is it normal to have different results when changing who is y1 , y2 , y3 , or am i doing something wrong?
2 if it is normal , does that mean i can have too many different particular solutions , just by changing who is y1 , y2 , y3?
 

Answers and Replies

  • #2
36,299
13,374
What are the different answers you get?
Maybe they are equivalent, and just look differently?
 
  • #3
omar yahia
9
0
What are the different answers you get?
Maybe they are equivalent, and just look differently?
:smile:
ummmmmm ... ahhhh .. actually ... when you asked me to show the results i went to prepare them for uploading
and as i was rewriting the solution i discovered an extra (2) multiplied in one little tiny term , will i fixed it and went on , and the results were the same indeed , i am terribly sorry for this mistake it happened because i trusted the solution of a senior without a thorough revision
thank you for your reply :smile: and i apologies again.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
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Never trust a senior!
 

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